Vibration behavior of a rotating non-uniform FG microbeam based on the modified couple stress theory and GDQEM

In this paper, for the first time, the size dependent vibration behavior of a rotating non-uniform functionally graded (FG) Timoshenko and Euler-Bernoulli microbeam based on the modified couple stress theory is presented. Also, the impact of the shear deformation on natural frequencies of the microbeam considering different values of the material length scale parameter, the angular velocity and the rate of cross section change is investigated. The mechanical and physical properties of the FG microbeam are varying along the thickness according to a power law equation. To determine governing equations, Hamilton's principle and a generalized differential quadrature element method (GDQEM) are applied. The natural frequencies of the microbeam for cantilever and propped cantilever boundary conditions are calculated. The accuracy and validity of the results are shown by several numerical examples. The influences of some parameters such as the small scale, the rate of cross section change, the angular velocity and the gradient index of the FG material on the first two natural frequencies, are plotted in several diagrams and are shown in tables. The results of this study can be used in designing and optimizing elastic and rotary type micro-electro-mechanical systems (MEMS) like micro-motors and micro-robots included rotating parts.